Image information about a body's internal structure may be determined non-invasively by radiation-based projection methods, for example computed tomography. The body may be the body of a patient, for example, whether human or animal. An inanimate object such as, for instance, a sample of material or a machine, may also be understood here as a body.
To be able to mutually differentiate the body's individual constituents, differences in said constituents are used in regard of their absorption characteristics in terms of the radiation with which the body is irradiated within the scope of the projection method. The body is therein thought of as being divided into what are termed voxels, which are small volume elements. For each of said voxels the absorption characteristic of the material located therein is then determined based on the projection-image data. The totality of such “attenuation values” for the individual voxels is here referred to as voxel data.
The voxel data are obtained by irradiating the body with the radiation from different directions and registering a projection image for each of said irradiating operations on a projection surface by means of, for example, electronic pixel sensors. Said projection images then each constitute a shadow of the body's individual elements. The projection-image data is nowadays usually assembled into a two-dimensional tomogram by means of what is termed filtered back projecting so that inferences may be made from the plurality of projection images about the nature of the body's materials in the individual voxels, i.e. the voxel data.
Filtered back projecting requires that the characteristics of the body's individual volume elements do not to change while the projection images are being recorded, often in succession, which means that the voxel data are independent of time. Hence, with that method it is not possible, for example, to show functionally, which is to say dynamically, how a contrast medium spreads along a patient's blood vessels. There being just a single projection image for each perfusion state of the contrast medium in the body, artifacts may appear during reconstructing of a tomographic image due to the temporal change in the voxel data.
An alternative approach to back projecting is offered using an algebraic reconstruction technique (ART). With that method it is possible to take account of there only ever being one projection image for a specific perfusion state of a contrast medium. An example of an ART algorithm of such kind is the method described in the work published by Neukirchen et al. (C. Neukirchen, M. Giordano, and S. Wiesner, “An Iterative Method for Tomographic X-ray Perfusion Estimation in a Decomposition Model-Based Approach”: Medical Physics, vol. 37, no. 12, pp. 6125-6141, December 2010). It is a method whereby the time-dependency of the voxel data representing the blood vessels in a patient's body is determined on the basis of a principal component analysis (PCA). The PCA is here used for determining basic functions for the course of the voxel values over time so that the time-dependent attenuation value in each voxel can then be described by superimposing said basic functions.